Let $M \subset \mathbb R^n$ be an oriented manifold of dimension $m$. Then the boundary $\partial M$ is an $(m-1)$-dimensional oriented manifold (with the induced orientation). Let $\phi U\to M$ be a local parametrization of $M$ near $p \in \partial M$ so that $0 \in U$ and $\phi(0) = p$, where $U$ is open in the half space $H^m_+$. A tangent vector \(v \in T_pM = D\phi(0)(\mathbb R^m)\subset\mathbb R^n\) is outward pointing if it is the image of a vector $w \in \mathbb R^m$ which does not lie in $H_+^m$.
Wikidata ID: Q2748415